Monodromy and Betti numbers of weighted complete intersections
Let (X,0) a weighted complete intersection of \(({\mathbb{C}}^ m,0)\), f: (X,0)\(\to ({\mathbb{C}},0)\) a holomorphic germ induced by a weighted homogeneous polynomial and \((X_ 0,0)=(f^{-1}(0),0)\). Assume that 0 is an isolated singularity of \((X_ 0,0)\), dim \(X_ 0\geq 1\). The aim of the paper is the investigation of the topology of \((X_ 0,0)\). More precisely, the monodromy operator associated to f is investigated extending results of Brieskorn, Hamm, Milnor and Orlik. Topological consequences are derived, e.g. the middle Betti number of the link of (X,0) is computed. Also the mixed Hodge structure of the Milnor fiber of (X,0) is computed (dim \(X\leq 3)\).
scientific article; zbMATH DE number 3957600